1 Answer
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It is possible. There are a lot of 20in wheel bikes with gears. There are some problems, though:

The frame might need to be opened so that the larger hub can be inserted;

There are no derailer hanger in bmx frames, so you'll have to use an adaptor, or a simpler derailer model which is mounted together with the axle;

The derailer itself is closer to the ground compared to 26in wheel bikes, but this might not be important, since many folding bikes are that way.

The least of your problems would be "looks"...

OR...

You can throw some more dollars and install an INTERNALLY GEARED HUB, which not just wouldn't break the clean looks, but would actually benefit from the horizontal dropouts found in BMX frames. But those are usually quite expensive.

And the geared hubs are probably still a bit fragile for true BMX use. Plus the geared hubs are quite large, and the spoke length would be quite short (leading to various problems) on a 20" wheel.
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Daniel R HicksJan 22 '13 at 18:00

Many years ago, I used to have derailier mechs that fitted on the axle with a lug that engaged the frame to stop it being pulled forward by the chain. Maybe those are still around? That might need a longer axle.
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DanSJan 23 '13 at 10:07